Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter β(τ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker–Bassett estimator minimizes a weighted distribut...

Efficiency Bounds for Semiparametric Estimation of Quantile Regression under Misspecification

Allowing for misspecification in the linear conditional quantile function (CQF), we calculate the semiparametric efficiency bound for the solution to the population quantile regression (QR) problem or the best linear predictor for a response variable under the asymmetric check loss function. The pseudo-true QR parameter that solves a non-differentiable unconditional moment restriction is interp...

Bayesian semiparametric additive quantile regression

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields po...

www.econstor.eu Bayesian semiparametric additive quantile regression

Semiparametric Quantile Regression with High-dimensional Covariates.

This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single-index structure. This semiparametric regression model enables us to reduce the dimension of the covariates and simultaneously retains the flexibility of nonparametric regression. Under mil...